566 BIBLIOGRAPHY OF HERSCHEL's WRITINGS. 



Herschel, W.: Synopsis of the Writings of— Contiuued. 



A. D. Vol. P. 



of the sixth maguitude to that of one of the seventh, is but httle 

 more than IJ to 1. 



1800 90 62 The faintness of the stars of the 7th magnitude gives us little room 

 to believe that we can penetrate much farther into space with ob- 

 jects of no greater brightness than stars. 

 63 I think, from the faintness of the stars of the 7th magnitude, and 

 from the foregoing considerations, we are authorized to conclude that 

 no star, eight, nine, or at most ten times as far from us as Sirius, 

 can possibly be perceived by the natural eye. 



63 Where the light of single stars falls short, however, the united lustre 



of sidereal systems will still be jjerceived. We easily see the united 

 lustre of the stars in the sword-haudlo of Perseus, though the light 

 of no one of the single stars could have aifected the unassisted eye. 



64 Perhaps, among the farthest objects that can make an impression on 



the eye, when not assisted by telescopes, may be reckoned the 

 nebula in the girdle of Andromeda discovered by Simon Map.ius in 

 1G12. 



64 It has been shown that brightness or light is to the naked ej'e truly 



represented by — .; in a telescoi^e, therefore, the light admitted will 



be expressed by --— . Hence it would follow that the artificial 



power of ^penetrating into space should be to the natural one as A 

 to a. But this proportion must be corrected by the practical defi- 

 ciency in light reflected and transmitted. 



65 As the result of many experiments with plane mirrors, polished like 



my large ones, and of the same composition of metal, I find we shall 

 have, in a telescope of my construction, with one reflection, 63,796 

 rays, out of 100,000 come to the eye. In the Newtonian form, 

 with a single eye-lens, 42,901 ; and, with a double eye-glass, 40,681 

 will remain for vision. 



65 Since the brightness of luminous objects is inversely as the squares 



of the distances, it follows that the penetrating power must be a3 

 the square roots of the light received by the eye. 



66 In natural vision, therefore, this power is truly expressed by VWT, 



and since we have now also obtained a jiroper correction ar, we must 

 apply it to the incident light with telescopes. 

 66 In the Newtonian and other constructions where two specula are 

 used there will also be some loss of light on account of the inter- 

 position of the small speculum ; therefore, putting h for its diameter, 

 we have a- h" f<^i" the real incident light. This being corrected as 



above, will give the general exx)ression V'jc/x A- &3 for the same 



power in telescopes. 

 66 Then, if we put natural light Z = 1, and divide by a, we have the 



general form '^•■^" "' for the penetrating power of all sorts of 



a 

 telescopes, compared to that of the natural eye as a standard. 



66 In the followiug investigation we .shall suppose a = two-tenths of an 



inch. 



67 "In the year 1776, when I had erected a telescope of 20 foot focal 



length, of the Newtonian construction, one of its effects by trial 

 was, that when towards evening, on account of darkness, the nat- 

 ural eye could not penetrate far into space, the telescope possessed 



